TransformPROOF.loop_after_pair: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend as TransformPROOF
Lines 913-940 of bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&start_line=913&end_line=940

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/layout.bend as Layout
import bendtorch-core@0.1.0.0/src/tensor/transform_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/transforms.bend as Transforms

def loop_after_pair(+fuel: Nat, +input: Shape.Shape, +axes: List<&2, U32>, +plan: Layout.Plan<input, axes>, +cursor: Nat,
  -original: Core.Tensor<input>, -before_source: Core.Tensor<input>, -before_target: Core.Tensor<Layout.output(input, axes, plan)>,
  -index: U32, -converted: {U32.to_nat(index) == cursor : Nat}, -candidate: {index == U32.from_nat(cursor) : U32},
  -prefix: Transforms.Prefix<input, axes, plan, original, before_source, before_target, cursor>,
  pair: Core.Tensor<input> & Result<&2, &1, Transforms.Error, Core.Tensor<Layout.output(input, axes, plan)>>,
  natural_exact: {Transforms.NaturalCopied{pair, index, converted, candidate} ==
    Transforms.natural_step(input, axes, plan, cursor, before_source, before_target) : Transforms.NaturalCopy<input, axes, plan, cursor>},
  -meaning: Transforms.StepMeaning(input, axes, plan, index, before_source, before_target, pair),
  rec: @source: Core.Tensor<input> -> @target: Core.Tensor<Layout.output(input, axes, plan)> ->
    @-prefix: Transforms.Prefix<input, axes, plan, original, source, target, 1n+cursor> ->
      Transforms.LoopCertificate<input, axes, plan, original, fuel, 1n+cursor, source, target>) ->
  Transforms.LoopCertificate<input, axes, plan, original, 1n+fuel, cursor, before_source, before_target>:
  (source, result) = pair
  match result:
    case Fail{error}:
      Transforms.LoopCertificate{(source, Fail{error}),
        Equal.cong(Transforms.NaturalCopy<input, axes, plan, cursor>,
          Core.Tensor<input> & Result<&2, &1, Transforms.Error, Core.Tensor<Layout.output(input, axes, plan)>>,
          step => Transforms.natural_next(input, axes, plan, cursor,
            source => target => Transforms.copy_loop(fuel, input, axes, plan, source, target, 1n+cursor), step),
          Transforms.NaturalCopied{(source, Fail{error}), index, converted, candidate},
          Transforms.natural_step(input, axes, plan, cursor, before_source, before_target), natural_exact), Unit{}}
    case Done{target}:
      loop_continue(fuel, input, axes, plan, cursor, original, before_source, before_target, source, target, index, converted, candidate,
        natural_exact, rec(source)(target)(
          Laws.advance_prefix(input, axes, plan, original, before_source, source, before_target, target, cursor, prefix,
            actual_advanced(input, axes, plan, cursor, original, before_source, source, before_target, target, prefix,
              canonical_step(input, axes, plan, cursor, index, before_source, before_target, source, target, candidate, converted, meaning)))))

Uses (26):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Unit
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=output
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_LAWS.bend&name=advance_prefix
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=actual_advanced
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=canonical_step
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=loop_continue
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=LoopCertificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=NaturalCopy
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=Prefix
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=StepMeaning
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=copy_loop
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=natural_next
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=natural_step